Methods of anchoring connecting elements in an opening in a fibrous or porous building material with the aid of mechanical vibrations are known from publications such as WO 98/00109, WO 00/79137 and WO 2006/002569, and for example from the international patent application PCT/CH 2007/000460. According to these methods a connecting element is placed in a prefabricated opening of the object or pressed against the surface of the object by a directed force, which in turn creates an opening. While a force acts upon the connecting element in the direction of an axis of the opening the element is excited by mechanical vibrations. The connecting element comprises thermoplastic material at least on one surface, which comes into contact with the material of the object during this procedure. The energy of the mechanical vibrations is set to liquefy thermoplastic material in the area of a predetermined anchoring point by mechanical vibrations and to press it into the pores or surface structures of the object by pressure building up at the anchoring point between a wall of the opening and the connecting element, thus forming a most effective macroscopic anchoring.